work, energy, and power in humans - openstax cnx module: m42153 1 work, energy, and power in humans...

Connexions module: m42153 1

Work, Energy, and Power in Humans∗

OpenStax College

This work is produced by The Connexions Project and licensed under the

Creative Commons Attribution License 3.0†

Abstract

• Explain the human body's consumption of energy when at rest vs. when engaged in activitiesthat do useful work.

• Calculate the conversion of chemical energy in food into useful work.

1 Energy Conversion in Humans

Our own bodies, like all living organisms, are energy conversion machines. Conservation of energy impliesthat the chemical energy stored in food is converted into work, thermal energy, and/or stored as chemicalenergy in fatty tissue. (See Figure 1.) The fraction going into each form depends both on how much we eatand on our level of physical activity. If we eat more than is needed to do work and stay warm, the remaindergoes into body fat.

Figure 1: Energy consumed by humans is converted to work, thermal energy, and stored fat. By far thelargest fraction goes to thermal energy, although the fraction varies depending on the type of physicalactivity.

∗Version 1.5: Feb 19, 2014 3:33 pm -0600†http://creativecommons.org/licenses/by/3.0/

http://cnx.org/content/m42153/1.5/


2 Power Consumed at Rest

The rate at which the body uses food energy to sustain life and to do di�erent activities is called themetabolic rate. The total energy conversion rate of a person at rest is called the basal metabolic rate(BMR) and is divided among various systems in the body, as shown in Table 1: Basal Metabolic Rates(BMR). The largest fraction goes to the liver and spleen, with the brain coming next. Of course, duringvigorous exercise, the energy consumption of the skeletal muscles and heart increase markedly. About 75%of the calories burned in a day go into these basic functions. The BMR is a function of age, gender, totalbody weight, and amount of muscle mass (which burns more calories than body fat). Athletes have a greaterBMR due to this last factor.

Basal Metabolic Rates (BMR)

Organ Power consumed atrest (W)

Oxygenconsumption(mL/min)

Percent of BMR

Liver & spleen 23 67 27

Brain 16 47 19

Skeletal muscle 15 45 18

Kidney 9 26 10

Heart 6 17 7

Other 16 48 19

Totals 85 W 250 mL/min 100%

Table 1

Energy consumption is directly proportional to oxygen consumption because the digestive process isbasically one of oxidizing food. We can measure the energy people use during various activities by measuringtheir oxygen use. (See Figure 2.) Approximately 20 kJ of energy are produced for each liter of oxygenconsumed, independent of the type of food. Table 2: Energy and Oxygen Consumption Rates1 (Power)shows energy and oxygen consumption rates (power expended) for a variety of activities.

3 Power of Doing Useful Work

Work done by a person is sometimes called useful work, which is work done on the outside world, suchas lifting weights. Useful work requires a force exerted through a distance on the outside world, and so itexcludes internal work, such as that done by the heart when pumping blood. Useful work does include thatdone in climbing stairs or accelerating to a full run, because these are accomplished by exerting forces onthe outside world. Forces exerted by the body are nonconservative, so that they can change the mechanicalenergy (KE + PE) of the system worked upon, and this is often the goal. A baseball player throwing a ball,for example, increases both the ball's kinetic and potential energy.

If a person needs more energy than they consume, such as when doing vigorous work, the body mustdraw upon the chemical energy stored in fat. So exercise can be helpful in losing fat. However, the amountof exercise needed to produce a loss in fat, or to burn o� extra calories consumed that day, can be large, asExample 1 (Calculating Weight Loss from Exercising) illustrates.

Example 1: Calculating Weight Loss from ExercisingIf a person who normally requires an average of 12,000 kJ (3000 kcal) of food energy per dayconsumes 13,000 kJ per day, he will steadily gain weight. How much bicycling per day is requiredto work o� this extra 1000 kJ?

1for an average 76-kg male



SolutionTable 2: Energy and Oxygen Consumption Rates2 (Power) states that 400 W are used when

cycling at a moderate speed. The time required to work o� 1000 kJ at this rate is then

Time =energy(energytime

) =1000 kJ

400 W= 2500 s = 42 min. (1)

DiscussionIf this person uses more energy than he or she consumes, the person's body will obtain the

needed energy by metabolizing body fat. If the person uses 13,000 kJ but consumes only 12,000kJ, then the amount of fat loss will be

Fat loss = (1000 kJ)(1.0 g fat

39 kJ

)= 26 g, (2)

assuming the energy content of fat to be 39 kJ/g.

Figure 2: A pulse oxymeter is an apparatus that measures the amount of oxygen in blood. Oxymeterscan be used to determine a person's metabolic rate, which is the rate at which food energy is convertedto another form. Such measurements can indicate the level of athletic conditioning as well as certainmedical problems. (credit: UusiAjaja, Wikimedia Commons)

Energy and Oxygen Consumption Rates3 (Power)

Activity Energy consumption inwatts

Oxygen consumption inliters O2/min

continued on next page

2for an average 76-kg male3for an average 76-kg male



Sleeping 83 0.24

Sitting at rest 120 0.34

Standing relaxed 125 0.36

Sitting in class 210 0.60

Walking (5 km/h) 280 0.80

Cycling (13�18 km/h) 400 1.14

Shivering 425 1.21

Playing tennis 440 1.26

Swimming breaststroke 475 1.36

Ice skating (14.5 km/h) 545 1.56

Climbing stairs (116/min) 685 1.96

Cycling (21 km/h) 700 2.00

Running cross-country 740 2.12

Playing basketball 800 2.28

Cycling, professional racer 1855 5.30

Sprinting 2415 6.90

Table 2

All bodily functions, from thinking to lifting weights, require energy. (See Figure 3.) The many smallmuscle actions accompanying all quiet activity, from sleeping to head scratching, ultimately become thermalenergy, as do less visible muscle actions by the heart, lungs, and digestive tract. Shivering, in fact, is aninvoluntary response to low body temperature that pits muscles against one another to produce thermalenergy in the body (and do no work). The kidneys and liver consume a surprising amount of energy, but thebiggest surprise of all it that a full 25% of all energy consumed by the body is used to maintain electricalpotentials in all living cells. (Nerve cells use this electrical potential in nerve impulses.) This bioelectricalenergy ultimately becomes mostly thermal energy, but some is utilized to power chemical processes such asin the kidneys and liver, and in fat production.



Figure 3: This fMRI scan shows an increased level of energy consumption in the vision center of thebrain. Here, the patient was being asked to recognize faces. (credit: NIH via Wikimedia Commons)

4 Section Summary

• The human body converts energy stored in food into work, thermal energy, and/or chemical energythat is stored in fatty tissue.

• The rate at which the body uses food energy to sustain life and to do di�erent activities is called themetabolic rate, and the corresponding rate when at rest is called the basal metabolic rate (BMR)

• The energy included in the basal metabolic rate is divided among various systems in the body, withthe largest fraction going to the liver and spleen, and the brain coming next.

• About 75% of food calories are used to sustain basic body functions included in the basal metabolicrate.

• The energy consumption of people during various activities can be determined by measuring theiroxygen use, because the digestive process is basically one of oxidizing food.

5 Conceptual Questions

Exercise 1Explain why it is easier to climb a mountain on a zigzag path rather than one straight up theside. Is your increase in gravitational potential energy the same in both cases? Is your energyconsumption the same in both?



Exercise 2Do you do work on the outside world when you rub your hands together to warm them? What isthe e�ciency of this activity?

Exercise 3Shivering is an involuntary response to lowered body temperature. What is the e�ciency of thebody when shivering, and is this a desirable value?

Exercise 4Discuss the relative e�ectiveness of dieting and exercise in losing weight, noting that most athleticactivities consume food energy at a rate of 400 to 500 W, while a single cup of yogurt can contain1360 kJ (325 kcal). Speci�cally, is it likely that exercise alone will be su�cient to lose weight? Youmay wish to consider that regular exercise may increase the metabolic rate, whereas protracteddieting may reduce it.

6 Problems & Exercises

Exercise 5 (Solution on p. 11.)

(a) How long can you rapidly climb stairs (116/min) on the 93.0 kcal of energy in a 10.0-g pat ofbutter? (b) How many �ights is this if each �ight has 16 stairs?

Exercise 6(a) What is the power output in watts and horsepower of a 70.0-kg sprinter who acceleratesfrom rest to 10.0 m/s in 3.00 s? (b) Considering the amount of power generated, do you think awell-trained athlete could do this repetitively for long periods of time?


Calculate the power output in watts and horsepower of a shot-putter who takes 1.20 s to acceleratethe 7.27-kg shot from rest to 14.0 m/s, while raising it 0.800 m. (Do not include the power producedto accelerate his body.)



Figure 4: Shot putter at the Dornoch Highland Gathering in 2007. (credit: John Haslam, Flickr)

Exercise 8(a) What is the e�ciency of an out-of-condition professor who does 2.10 × 105 J of useful workwhile metabolizing 500 kcal of food energy? (b) How many food calories would a well-conditionedathlete metabolize in doing the same work with an e�ciency of 20%?


Energy that is not utilized for work or heat transfer is converted to the chemical energy of bodyfat containing about 39 kJ/g. How many grams of fat will you gain if you eat 10,000 kJ (about2500 kcal) one day and do nothing but sit relaxed for 16.0 h and sleep for the other 8.00 h? Usedata from Table 2: Energy and Oxygen Consumption Rates4 (Power) for the energy consumptionrates of these activities.

Exercise 10Using data from Table 2: Energy and Oxygen Consumption Rates5 (Power), calculate the dailyenergy needs of a person who sleeps for 7.00 h, walks for 2.00 h, attends classes for 4.00 h, cyclesfor 2.00 h, sits relaxed for 3.00 h, and studies for 6.00 h. (Studying consumes energy at the samerate as sitting in class.)


What is the e�ciency of a subject on a treadmill who puts out work at the rate of 100 W whileconsuming oxygen at the rate of 2.00 L/min? (Hint: See Table 2: Energy and Oxygen ConsumptionRates6 (Power).)

Exercise 12Shoveling snow can be extremely taxing because the arms have such a low e�ciency in this activity.Suppose a person shoveling a footpath metabolizes food at the rate of 800 W. (a) What is her usefulpower output? (b) How long will it take her to lift 3000 kg of snow 1.20 m? (This could be the

4for an average 76-kg male5for an average 76-kg male6for an average 76-kg male



amount of heavy snow on 20 m of footpath.) (c) How much waste heat transfer in kilojoules willshe generate in the process?


Very large forces are produced in joints when a person jumps from some height to the ground. (a)Calculate the magnitude of the force produced if an 80.0-kg person jumps from a 0.600�m-high ledgeand lands sti�y, compressing joint material 1.50 cm as a result. (Be certain to include the weightof the person.) (b) In practice the knees bend almost involuntarily to help extend the distance overwhich you stop. Calculate the magnitude of the force produced if the stopping distance is 0.300 m.(c) Compare both forces with the weight of the person.

Exercise 14Jogging on hard surfaces with insu�ciently padded shoes produces large forces in the feet and legs.(a) Calculate the magnitude of the force needed to stop the downward motion of a jogger's leg, ifhis leg has a mass of 13.0 kg, a speed of 6.00 m/s, and stops in a distance of 1.50 cm. (Be certainto include the weight of the 75.0-kg jogger's body.) (b) Compare this force with the weight of thejogger.


(a) Calculate the energy in kJ used by a 55.0-kg woman who does 50 deep knee bends in whichher center of mass is lowered and raised 0.400 m. (She does work in both directions.) You mayassume her e�ciency is 20%. (b) What is the average power consumption rate in watts if she doesthis in 3.00 min?

Exercise 16Kanellos Kanellopoulos �ew 119 km from Crete to Santorini, Greece, on April 23, 1988, in theDaedalus 88, an aircraft powered by a bicycle-type drive mechanism (see Figure 5). His usefulpower output for the 234-min trip was about 350 W. Using the e�ciency for cycling from here7,calculate the food energy in kilojoules he metabolized during the �ight.

7"Conservation of Energy": Table 2: E�ciency of the Human Body and Mechanical Devices<http://cnx.org/content/m42151/latest/#import-auto-id1330125>



Figure 5: The Daedalus 88 in �ight. (credit: NASA photo by Beasley)


The swimmer shown in Figure 6 exerts an average horizontal backward force of 80.0 N with hisarm during each 1.80 m long stroke. (a) What is his work output in each stroke? (b) Calculate thepower output of his arms if he does 120 strokes per minute.

Figure 6

Exercise 18Mountain climbers carry bottled oxygen when at very high altitudes. (a) Assuming that a

mountain climber uses oxygen at twice the rate for climbing 116 stairs per minute (because of lowair temperature and winds), calculate how many liters of oxygen a climber would need for 10.0 h



of climbing. (These are liters at sea level.) Note that only 40% of the inhaled oxygen is utilized;the rest is exhaled. (b) How much useful work does the climber do if he and his equipment have amass of 90.0 kg and he gains 1000 m of altitude? (c) What is his e�ciency for the 10.0-h climb?


The awe-inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its squarebase, originally 230 m on a side, covered 13.1 acres, and it was 146 m high, with a mass of about7 × 109 kg. (The pyramid's dimensions are slightly di�erent today due to quarrying and somesagging.) Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hourdays, 330 days per year. (a) Calculate the gravitational potential energy stored in the pyramid,given its center of mass is at one-fourth its height. (b) Only a fraction of the workers lifted blocks;most were involved in support services such as building ramps (see Figure 7), bringing food andwater, and hauling blocks to the site. Calculate the e�ciency of the workers who did the lifting,assuming there were 1000 of them and they consumed food energy at the rate of 300 kcal/h. Whatdoes your answer imply about how much of their work went into block-lifting, versus how muchwork went into friction and lifting and lowering their own bodies? (c) Calculate the mass of foodthat had to be supplied each day, assuming that the average worker required 3600 kcal per day andthat their diet was 5% protein, 60% carbohydrate, and 35% fat. (These proportions neglect themass of bulk and nondigestible materials consumed.)

Figure 7: Ancient pyramids were probably constructed using ramps as simple machines. (credit: FranckMonnier, Wikimedia Commons)

Exercise 20(a) How long can you play tennis on the 800 kJ (about 200 kcal) of energy in a candy bar? (b)Does this seem like a long time? Discuss why exercise is necessary but may not be su�cient tocause a person to lose weight.



Solutions to Exercises in this Module

Solution to Exercise (p. 6)(a) 9.5 min

(b) 69 �ights of stairsSolution to Exercise (p. 6)641 W, 0.860 hpSolution to Exercise (p. 7)31 gSolution to Exercise (p. 7)14.3%Solution to Exercise (p. 8)(a) 3.21× 104 N

(b) 2.35× 103 N(c) Ratio of net force to weight of person is 41.0 in part (a); 3.00 in part (b)

Solution to Exercise (p. 8)(a) 108 kJ

(b) 599 WSolution to Exercise (p. 9)(a) 144 J

(b) 288 WSolution to Exercise (p. 10)(a) 2.50× 1012 J

(b) 2.52%(c) 1.4× 104 kg (14 metric tons)

Glossary

De�nition 1: metabolic ratethe rate at which the body uses food energy to sustain life and to do di�erent activities

De�nition 2: basal metabolic ratethe total energy conversion rate of a person at rest

De�nition 3: useful workwork done on an external system


work, energy, and power in humans - openstax cnx module: m42153 1 work, energy, and power in humans...

Documents